# Projectile motion: determine launch angle

1. Jan 15, 2014

### justsway17

1. The problem statement, all variables and given/known data

A cannon is supported one meter above the top of a 20 degree declining slope of length 200m. The cannon has a launch velocity of 55m/s. There is a ball halfway down this slope moving at a constant velocity of 20m/s.

-Determine the angle $\Theta$ required for the projectile to hit the bottom of the hill within one degree.
-How long does the projectile take to hit the bottom of the hill?
-There is a target moving at a constant velocity of 20m/s down the hill. How long should you delay firing to hit the target as it reaches the bottom of the hill?
-Find the maximum distance this projectile can travel as measured from the bottom of the hill.

2. Relevant equations

x=x$_{0}$+v$_{0x}$t
v$_{y}$=v$_{0y}$t-gt$^{2}$
y=y$_{0}$+v$_{0y}$t-0.5gt$^{2}$
v$^{2}_{y}$=v$^{2}_{0y}$-2g(y-y$_{0}$)

3. The attempt at a solution

I have tried using all of the two-dimensional kinematics equations with some success but the problem is that $\Theta$ is unknown so I can't find t or v$_{fy}$.

My best attempts are as so:
v$_{yf}$=55sin$\Theta$-9.81t
188=55cos($\Theta$)t
188=0+55cos($\Theta$)t-4.9t$^{2}$

The diagram for the problem is attached.
Either it is algebra more complicated than I am used to or I am missing something very simple. I am confident that if I could solve for $\Theta$ OR t I could finish the problem easily. I can't seem to get a solveable equation. Thank you for your help and I apologize if there are syntax errors as I am a first time user.

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Last edited: Jan 15, 2014
2. Jan 15, 2014

### yands

There is inconsistency , the questions on the attachment and the problem statement you provided . I would like to help you but there are some ambiguity .

3. Jan 15, 2014

### justsway17

I apologize for that. I just updated the post to match the wording of the diagram exactly. I have continued to work on this problem and used a few pages of paper, but still have not been able to find a way to solve for theta.

4. Jan 15, 2014

### yands

You have to find the range in terms of the initial angle then try to optimize it . That is how I solved it . You have to think why one needs an optimization approach to solve this problem.